A global methodology for the modal reduction of large nonlinear systems containing quadratic and cubic nonlinearities

Proceedings of the ASME Design Engineering Technical Conference

Volumn 1A-1997, Issue , 1997, Pages

  Pesheck, E ^a   Pierre, C ^b  

^a University of Michigan   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MODAL ANALYSIS; PHASE SPACE METHODS; POLYNOMIAL APPROXIMATION;

ARBITRARY SYSTEMS; CUBIC NONLINEARITIES; HARMONIC FORCING; HIGH-DIMENSIONAL; MODAL COORDINATES; MODAL TRUNCATION; ORIGINAL SYSTEMS; STRUCTURAL SYSTEMS;

VIBRATIONS (MECHANICAL);

EID: 85051988545     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC97/VIB-3952     Document Type: Conference Paper

References (12)

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2. Boivin, N., 1995, "Non-linear Modal Analysis of Structural Systems Using Invariant Manifolds," PhD. Dissertation, The University of Michigan, Ann Arbor, MI
3. Boivin, N, Pierre, C., and Shaw, S. W., 1995, "Non-Linear Normal Modes, Invariance, and Modal Dynamics Approximations of Non-Linear Systems," Nonlinear Dynamics Vol. 8; pp. 315-346
4. = &J + Boivin, N, Pierre, C., and Shaw, S. W., 1995, "Non-Linear Modal Analysis of Structural Systems Featuring Internal Resonances," J. of Sound and Vibration Vol. 182(2); pp. 336-341
5. King, M. E., and Vakakis, A. F., 1994, "An Energy Based Formulation for Computing Nonlinear Normal Modes in Undamped Continuous Systems," J. of Vibration and Acoustics, Transactions of the ASME Vol. 116, pp. 332-340
6. Nayfeh, A. H., Chin, C., and Nayfeh, S. A., 1996, "On Nonlinear Normal Modes of Systems with internal Resonance," Journal of Vibrations and Acoustics, Transactions of the ASME Vol. 118, pp. 340-345
7. Rosenberg, R. M., 1966, "On Nonlinear Vibrations of Systems with Many Degrees of Freedom." Advances in Applied Mechanics Vol. 9, pp. 155-242
8. Shaw, S. W. and Pierre, C., 1991, "Non-linear Normal Modes and Invariant Manifolds," J. of Sound and Vibration Vol. 150(l), pp. 170-173
9. Shaw, S. W. and Pierre, C., 1993, "Normal Modes for Non-Linear Vibratory Systems," J. of Sound and Vibration Vol. 164(l), pp. 85-124
10. Shaw, S. W., 1994, "An Invariant Approach to Nonlinear Normal Modes of Vibration," J. of Nonlinear Science Vol. 4, pp. 419-448
11. Slater, J. C., 1996, "A Numerical Method for Determining Nonlinear Normal Modes," Nonlinear Dynamics Vol. 10, pp. 29-30
12. Vakakis, A. F., 1996, Normal Modes and Localization in Nonlinear Systems, John Wiley & Sons